If an equation of the linear function is y = mx + b, then what is m?
Straight lines are very important concepts in mathematics which are represented by linear equations in a cartesian plane. They have a constant slope.
Answer: If an equation of the linear function in the figure above is y = mx + b, then m is the slope of the line.
Let's understand the solution in detail.
The equation y = mx + b is a linear equation; hence it represents a straight line. Any point (x1, y1) on this line must satisfy this equation as
⇒ y1 = mx1 + b ---------- (1)
Now let's take a random point P(x2, y2) on the given line. Now we have:
⇒ y2 = mx2 + b ---------- (2)
Now if we find (2 - 1), we get y2 - y1 = m (x2 - x1)
Hence, m = (y2 - y1) / (x2 - x1)
This formula denotes the change in the vertical coordinates divided by the change in the horizontal coordinates which is the definition for slope.